The PPT square conjecture holds generically for some classes of independent states

Benoît Collins, Zhi Yin, Ping Zhong

Let $|\psi ⟩⟨\psi |$ be a random pure state on ${\mathbb{C}}^{d^2}\otimes {\mathbb{C}}^s$, where $\psi$ is a random unit vector uniformly distributed on the sphere in $\mathbb{C}^{d^…